Exotic Hadrons: models applied to LHCb pentaquarks
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1 Exotic Hadrons: models applied to LHCb pentaquarks Tim Burns Swansea University 6 September 017 [T.B., Eur.Phys.J. A51, 15 (015), ] [T.B. & E.Swanson (ongoing)]
2 Conventional and exotic hadrons
3 Conventional and exotic hadrons Baryons Mesons
4 Conventional and exotic hadrons Baryons Mesons
5 Conventional and exotic hadrons Hybrids
6 Conventional and exotic hadrons Hybrids Compact multiquarks
7 Conventional and exotic hadrons Hybrids Compact multiquarks Hadronic molecules
8 Conventional and exotic hadrons Hybrids Compact multiquarks Hadronic molecules Threshold eect
9 P c (4380) and P c (4450)
10 P c (4380) and P c (4450) LHCb amplitude analysis of the three-body decay Λ b J/ψpK. [LHCb,PRL115,07001,015] u d b u d u ū s c c p K J/ψ Two J/ψp states, the avour of the proton with hidden charm (uudc c).
11 P c (4380) and P c (4450) P c (4380) + P c (4450) + Mass 4380 ± 8± ± 1.7 ±.5 Width 05 ± 18 ± ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/
12 Compact pentaquark
13 Compact pentaquark The uudc c combination in S-wave gives: I (J P ) ( ) ( ( ( ( ( ) ) ) ) )
14 Compact pentaquark
15 Compact pentaquark
16 Compact pentaquark
17 Threshold eect
18 Threshold eect P c (4380) + P c (4450) + Mass 4380 ± 8± ± 1.7 ±.5 Width 05 ± 18 ± ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/
19 Threshold eect P c (4380) + P c (4450) + Mass 4380 ± 8± ± 1.7 ±.5 Width 05 ± 18 ± ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/ Σ + c D 0 (udc)(u c) ±.4 Σ + D c 0 (udc)(u c) ± 0.5 Λ + c (1P) D 0 (udc)(u c) ± 0.35 χ c1 p (udu)(c c) ± 0.07
20 Threshold eect u d b u d c s c
21 Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p
22 Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p c c b u d s u d
23 Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p b u d c c s u d Λ b Λ J/ψ, χ c,... p K J/ψ p
24 Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p b u d u b d c c s u d ū c s c d Λ b Λ J/ψ, χ c,... p K J/ψ p
25 Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p b u d u b d c c s u d ū c s c d Λ b Λ b Λ Ξ c J/ψ, χ c,... p K D Λ c /Σ c K J/ψ p J/ψ p
26 Threshold eect Enhancements expected at Λ c D = 1/ Λ c D = 1/, 3/ not seen at LHCb Λ b D s Λ c D K J/ψ p J/ψ, χ c,... J/ψ Λ b Λ p K p D J/ψ Λ b Ξ c Λ c /Σ c K p
27 Threshold eect Λ c (1P) D P c (4450) mass, but S-wave = 1/ + Λ b P-wave = 1/, 3/ why no Λ c (1P) D states? D s Λ c D K J/ψ p J/ψ, χ c,... J/ψ Λ b Λ p K p D J/ψ Λ b Ξ c Λ c /Σ c K p
28 Threshold eect Λ c (1P) D P c (4450) mass, but S-wave = 1/ + Λ b P-wave = 1/, 3/ why no Λ c (1P) D states? D s Λ c D K J/ψ p χ c1 p = P c (4450) mass, but doubly suppressed S-wave = 1/ +, 3/ + P-wave = 1/, 3/, 5/ Λ b Λ J/ψ, χ c,... p K J/ψ p D J/ψ Λ b Ξ c Λ c /Σ c K p
29 Threshold eect Λ c (1P) D P c (4450) mass, but S-wave = 1/ + Λ b P-wave = 1/, 3/ why no Λ c (1P) D states? D s Λ c D K J/ψ p χ c1 p = P c (4450) mass, but doubly suppressed S-wave = 1/ +, 3/ + P-wave = 1/, 3/, 5/ Λ b Λ J/ψ, χ c,... p K J/ψ p Σ c D P c (4380) mass, and Σ c D P c (4450) mass, but doubly suppressed what restricts J P? why not Σ c D, Σ c D? Λ b Ξ c D Λ c /Σ c K J/ψ p
30 Hadronic molecule
31 Hadronic molecule Consider the deuteron, a 0(1 ) state. MeV below pn threshold. vs.
32 Hadronic molecule P c (4380) + P c (4450) + Mass 4380 ± 8± ± 1.7 ±.5 Width 05 ± 18 ± ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/ Σ + c D 0 (udc)(u c) ±.4 Σ + D c 0 (udc)(u c) ± 0.5 Λ + c (1P) D 0 (udc)(u c) ± 0.35 χ c1 p (udu)(c c) ± 0.07
33 Hadronic molecule P c (4380) + P c (4450) + Mass 4380 ± 8± ± 1.7 ±.5 Width 05 ± 18 ± ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/ Σ + c D 0 (udc)(u c) ±.4 Σ + D c 0 (udc)(u c) ± 0.5 Λ + c (1P) D 0 (udc)(u c) ± 0.35 χ c1 p (udu)(c c) ± 0.07
34 Hadronic molecule P c (4380) + P c (4450) + Mass 4380 ± 8± ± 1.7 ±.5 Width 05 ± 18 ± ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/ Σ + c D 0 (udc)(u c) ±.4 Σ + D c 0 (udc)(u c) ± 0.5 Λ + c (1P) D 0 (udc)(u c) ± 0.35 χ c1 p (udu)(c c) ± 0.07
35 Hadronic molecule The (udc)(u c) combinations in S-wave are: I (J P ) Λ c D Λ c D Σ c D Σ D c Σ c D Σ D c ( ) ( ( ( ( ( ) ) ) ) )
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39 Hadronic molecule Forbidden vertices: Λ c Λ c (isospin) π D D (spin-parity) π
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42 Hadronic molecule c u d c u d Λ c, Σ c, Σ c π π u c u c D, D V ( r) = ij [ C(r) σi σ j + T (r)s ij (ˆr) ] τ i τ j
43 Hadronic molecule c u d c u d Λ c, Σ c, Σ c π π V ( r) = ij u c u c [ C(r) σi σ j + T (r)s ij (ˆr) ] τ i τ j D, D All I = 3/ potentials suppressed by 1/.
44 Hadronic molecule c u d c u d Λ c, Σ c, Σ c π π V ( r) = ij u c u c [ C(r) σi σ j + T (r)s ij (ˆr) ] τ i τ j D, D All I = 3/ potentials suppressed by 1/. Coecient of C(r) is important.
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54 Hadronic molecule I (J P ) Λ c D Λ c D Σ c D Σ c D Σ c D Σ c D 1 ( 1 ) 1 ( 3 ) 1 ( 5 ) 3 ( 1 ) 3 ( 3 ) 3 ( 5 )
55 Hadronic molecule I (J P ) Λ c D Λ c D Σ c D Σ c D Σ c D Σ c D 1 ( 1 ) 1 ( 3 ) 1 ( 5 ) 3 ( 1 ) 3 ( 3 ) 3 ( 5 )
56 Hadronic molecule I (J P ) Λ c D Λ c D Σ c D Σ c D Σ c D Σ c D 1 ( 1 ) 1 ( 3 ) 1 ( 5 ) 3 ( 1 ) 3 ( 3 ) 3 ( 5 )
57 Hadronic molecule I (J P ) Λ c D Λ c D Σ c D Σ c D Σ c D Σ c D 1 ( 1 ) 1 ( 3 ) P c (4450)? 1 ( 5 ) 3 ( 1 ) 3 ( 3 ) 3 ( 5 )
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68 Summary exotic-ness high! low medium d.o.f. quarks hadrons hadrons interactions g exchange rescattering π exchange colour (1 1) (8 8) (1 1) (1 1) size compact extended masses model dependent at thresholds at thresholds J PC all restricted restricted avours all restricted restricted(i -mix) channels most restricted HQ restricted falsiability low medium high
69 Backup slides
70 Ξ c D molecules Λ c = ((ud) 0 c) 1/ = Ξ c = ((us) 0 c) 1/ Σ c = ((ud) 1 c) 1/ = Ξ c = ((us) 1 c) 1/ Σ c = ((ud) 1 c) 3/ = Ξ c = ((us) 1 c) 3/ c u d c u s π = π u c u c The potential matrices (central + tensor) are directly related. Predict loosely bound 0(5/ ) Ξ c D state, observable in Λ b J/ψΛη.
71 Isospin mixing: P c (4380) and P c (4450) uudc c comes in two charge combinations { (udc)(u c) = Σ + c D 0 (uuc)(d c) = Σ ++ c D Isospin-conserving interactions would produce I, I 3 eigenstates, ( 1, 1 ) 3, 1 = ( ) Σ + c D 0 Σ ++ c D but only if the masses Σ + c = Σ ++ c and D 0 = D Otherwise, isospin is not a good quantum number.
72 Isospin mixing: P c (4380) and P c (4450) Σ + c D 0 = ±.4 Σ + c D 0 = ± 0.5 Σ ++ c D = ± 0.7 Σ ++ c D = ± 0.3
73 Isospin mixing: P c (4380) and P c (4450) P c (4380) = 4380 ± 8 ± 9 P c (4450) = 4449 ± 1.7 ±.5 D 0 = ±.4 Σ + D c 0 = ± 0.5 Σ + c Σ ++ c D = ± 0.7 Σ ++ c D = ± 0.3
74 Isospin mixing: P c (4380) and P c (4450) P c (4380) = 4380 ± 8 ± 9 P c (4450) = 4449 ± 1.7 ±.5 D 0 = ±.4 Σ + D c 0 = ± 0.5 Σ + c Σ ++ c D = ± 0.7 Σ ++ c D = ± 0.3 The P c states have mixed isospin: P c = cos φ 1, 1 + sin φ 3, 1
75 Isospin mixing: P c (4380) and P c (4450) P c (4380) = 4380 ± 8 ± 9 P c (4450) = 4449 ± 1.7 ±.5 D 0 = ±.4 Σ + D c 0 = ± 0.5 Σ + c Σ ++ c D = ± 0.7 Σ ++ c D = ± 0.3 The P c states have mixed isospin: P c = cos φ 1, 1 + sin φ 3, 1 They should decay also into J/ψ + and η c +, with weights: J/ψp : J/ψ + : η c + = cos φ : 5 sin φ : 3 sin φ [P c (4380)] J/ψp : J/ψ + : η c + = cos φ : 10 sin φ : 6 sin φ [P c (4450)]
76 Isospin mixing: predicted 5/ states Σ c D 1/(5/ ) Σ + c D 0 = ±.4 Σ ++ c D = 458. ± 0.7 Mixed isopsin: P = cos φ 1, 1 + sin φ 3, 1 Decays: J/ψp: D-wave, spin ip Reason for absence at LHCb? J/ψ : S-wave, spin cons. = I = 3/ decay enhanced.
77 Isospin mixing: predicted 5/ states Σ c D 1/(5/ ) Ξ c D 0(5/ ) Σ + c D 0 = ±.4 Σ ++ c D = 458. ± 0.7 Ξ 0 c D 0 = ± 0.6 Ξ + c D = ± 0.7 Mixed isopsin: P = cos φ 1, 1 + sin φ 3, 1 Mixed isopsin: P = cos φ 0, 0 + sin φ 1, 0 Decays: J/ψp: D-wave, spin ip Reason for absence at LHCb? Decays: J/ψΛ: D-wave, spin ip e.g. Λ 0 b J/ψΛη, J/ψΛφ J/ψ : S-wave, spin cons. = I = 3/ decay enhanced. J/ψΣ : S-wave, spin cons. = I = 1 decay enhanced.
78 Pion exchange: central potential C(r) r(gev 1 ) Yukawa
79 Pion exchange: central potential C(r) without delta term C(r) with delta term 1 GeV r(gev 1 ) GeV Yukawa
80 Pion exchange: central potential C(r) without delta term C(r) with delta term 1 GeV r(gev 1 ) GeV +C(r) Yukawa +C(r)
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